EVALUASI NUMERIK PENDUGA FUNGSI NILAI HARAPAN DAN FUNGSI RAGAM PROSES POISSON MAJEMUK DENGAN INTENSITAS EKSPONENSIAL FUNGSI LINEAR
Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be 𝑒𝑥𝑝(𝛼+𝛽𝑠) with 0<𝛽<∞, where 𝛽 is assumed to be known. In , estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to 1−𝛼 of the probabilities that the parameters are contained in the confidence intervals constructed in . Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level 𝛼, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to 1−𝛼.